This paper deals with the issue of correlated noises in GPS navigation. GPS is based on the measure of the propagation delays of satellite signals. Therefore, additional delays induced when traveling through the ionosphere or the troposphere degrade GPS accuracy. These error sources are correlated, both spatially and temporally. Thus, when using an extended Kalman filter as navigation algorithm, these correlations should be taken into account to ensure that an optimal solution is obtained in terms of mean square error. Our contribution is to study, in this context, the relevance of an alternative approach well-known in the field of control engineering: the H1 filter. Also based on a state representation, this technique has the advantage of relaxing the constraints on the measurement and state noises. A comparative study with a standard extended Kalman filter and a colored extended Kalman filter is carried out to illustrate which of the above-mentioned approaches achieves the better compromise between accuracy and computational complexity.